<h2>Problem 112</h2>
<div style="color:#666;font-size:80%;">30 December 2005</div><br />
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<p>Working from left-to-right if no digit is exceeded by the digit to its left it is called an increasing number; for example, 134468.</p>
<p>Similarly if no digit is exceeded by the digit to its right it is called a decreasing number; for example, 66420.</p>
<p>We shall call a positive integer that is neither increasing nor decreasing a &quot;bouncy&quot; number; for example, 155349.</p>
<p>Clearly there cannot be any bouncy numbers below one-hundred, but just over half of the numbers below one-thousand (525) are bouncy. In fact, the least number for which the proportion of bouncy numbers first reaches 50% is 538.</p>
<p>Surprisingly, bouncy numbers become more and more common and by the time we reach 21780 the proportion of bouncy numbers is equal to 90%.</p>
<p>Find the least number for which the proportion of bouncy numbers is exactly 99%.</p>

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